 | 1801 - 650 pages
...sides of a plane triangle are the shortest distances between the angular points on a plane. Therefore the sum of any two sides of a spherical triangle is greater than the third. Q._ ED f DEMONSTRATION. Let the sides AB, AC, containing any angle A, be produced till they meet again... | |
 | Thomas Leybourn - 1817 - 454 pages
...third zq л minimum, which is evidently the case when equal to the difference between qs, zs, because the sum of any two sides of a spherical triangle is greater than the third. Consequently, when the elapsed time is a minimum, gz i* equal to the difference between the altitudes... | |
 | James Mitchell - 1823 - 670 pages
...the less side. 2. Any side or angle of a spherical triangle is less than a semicircle, or 180°. 3. The sum of any two sides of a spherical triangle is greater than the third side; and their difference is less than the third side. 4. The dilference of any two Aides of a spherical triangle... | |
 | William Galbraith - 1827 - 430 pages
...been long meditated. PROPOSITION XV. 36. The sum of any two sides of a spherical triangle is gïeater' than the third side ; and the difference of any two sides is less than the third side. Cor. — The shortest distance between any two points on the surface of a sphere is the arc which passes... | |
 | Dionysius Lardner - 1828 - 430 pages
...(127.) Any two sides of a spherical triangle are together greater than the third side. (128.) Cor. The difference of any two sides is less than the third side. (129.) The sum of the three sides is less than the circumference of a great circle. (130.) Cor. The... | |
 | James Hayward - 1829 - 228 pages
...(220) the sum of the arcs which measure them must be greater than the third arc (113) ; that is— The sum of any two sides of a spherical triangle, is greater than the third. Whence we infer that—The shortest way from one point to another, on the surface of a sphere, is in... | |
 | Alexander Ingram - 1830 - 460 pages
...sides opposite to them are also equal. PROP. VIII. Any two sides of a spherical triangle are together greater than the third side, and the difference of any two sides is less than the third. Cor. The arc which passes through any two points on the surface of a sphere is the shortest distance... | |
 | William Galbraith - 1834 - 454 pages
...angles of another, each to each, their remaining sides and angles will be equal. PROPOSITION XV. 36. The sum of any two sides of a spherical triangle is...difference of any two sides is less than the third side. Cor. — The shortest distance between any two points on the surface of a sphere is the arc which passes... | |
 | Charles Bonnycastle - 1834 - 670 pages
...polygon. Whence the following propositions : RELATIONS COMMON TO ALL SPHERICAL TRIANGLES. 185 — 1. The sum of any two sides of a spherical triangle is greater than the third side ; art. 157 — 1. 2. The sum of the three sides is less than unity ; art. 157—2. 3. The sum of the... | |
 | Nathan Scholfield - 1845 - 542 pages
...— cos. *' is always positive. Again, if a', 6', c', be the three sides of the polar triangle, since the sum of any two sides of a spherical triangle is greater than the third side : I b' + c1 > a1 .-. 180° — B+1800 — C > 180° — A .v B+ C — A< 180° */ — cos. s' cos.... | |
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The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. 
